Physics Q96 – AP-EAMCET 2026

Home Physics Thermal PropertiesQuestion #487

How much should the temperature of a metal ring of diameter

100 cm

to be raised in order to fit it on a wooden disc of diameter

100.6 cm

[coefficient of linear expansion of metal =

12 \times 10^{- 6} {\degree C}^{- 1}

]

Clue 1 of 3: Thermal Expansion

When a material is heated, its dimensions (length, area, volume) generally increase. This phenomenon is called thermal expansion. For a linear dimension like diameter, it expands proportionally to the initial length, the temperature change, and the material's coefficient of linear expansion.

🧠 Full Solution Path

Step 1: Identify Given Parameters and Goal✦ Active

Identify the initial diameter of the metal ring ( $D_{0}$ ), the final desired diameter ( $D_{f}$ ), and the coefficient of linear expansion ( $α$ ). The goal is to find the change in temperature ( $Δ T$ ) required for the ring to expand to the desired size.

D_{0} = 100 cm

D_{f} = 100.6 cm

α = 12 \times 10^{- 6} {\degree C}^{- 1}

Find Δ T

💡 Teacher's Secret Hint

Remember that $Δ T$ represents the *change* in temperature, not the final temperature. If an initial temperature were given, we would add $Δ T$ to it to find the final temperature.

Step 2: Calculate the Required Change in Diameter○ Expand

Determine how much the diameter of the ring needs to increase by subtracting the initial diameter from the final desired diameter.

Δ D = D_{f} - D_{0}

Δ D = 100.6 cm - 100 cm

Δ D = 0.6 cm

Step 3: Apply the Linear Thermal Expansion Formula○ Expand

Use the formula for linear thermal expansion, which relates the change in length (or diameter) to the initial length, the coefficient of linear expansion, and the change in temperature.

Δ D = D_{0} α Δ T

💡 Teacher's Secret Hint

In this formula, the units of $D_{0}$ and $Δ D$ must be consistent (e.g., both in cm or both in meters), and the unit of $α$ must be consistent with the unit of temperature change (e.g., ${\degree C}^{- 1}$ for $Δ T$ in $\degree C$ ). Also, note that the linear expansion applies to the diameter as well as the circumference of the ring.

Step 4: Solve for the Change in Temperature (

Δ T

)○ Expand

Rearrange the formula from the previous step to solve for $Δ T$ and substitute the known values.

Δ T = \frac{Δ D}{D_{0} α}

Δ T = \frac{0.6 cm}{100 cm \times 12 \times 10^{- 6} {\degree C}^{- 1}}

Δ T = \frac{0.6}{1200 \times 10^{- 6}}

Δ T = \frac{0.6}{1.2 \times 10^{- 3}}

Δ T = 500 \degree C

💡 Teacher's Secret Hint

Pay attention to the powers of ten and unit cancellation. The 'cm' units cancel out, leaving the result in $\degree C$ . A common mistake is to forget to convert units or to miscalculate the exponent in scientific notation.

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Physics Question 96 – AP-EAMCET 2026

Clue 1 of 3: Thermal Expansion

🧠 Full Solution Path